On the numerical approximation of hyperbolic mean curvature flows for surfaces

Abstract

The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in ${\mathbb{R}}^3$. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the case of axially symmetric surfaces. We present a number of numerical simulations, including convergence tests as well as simulations suggesting the onset of singularities.

26 pages, 12 figures